So, AMD is lying, basically? Btw, the CPU in question does run at 5Ghz, I don't see the issue.
I've found a link which might help it make more sense.
But I will try to pad it out myself, then bring in the link.
The colour information (for the pixel)
IS 128-bit floating point precision. (But this means 4 lots of 32 bit floating point, combined into one 128 bit register/memory).
BUT the colour information consists of individual values, such as RED, green, blue etc, each of which are actually 32-bit single floating point values.
So the spec sheets say stuff like (the final link, is where all these quotes come from):
The combined colour information is:
128-bit IEEE floating-point precision graphics pipeline
But each combined colour information (for a single pixel), actually is made up of:
32-bit floating point color precision per component
I.e. Each component is 32 bits of floating point precision, when all 4 colour values/attributes are combined, they make a 128-bit floating point value (which is precise to a maximum of 32 bits, per component).
All quotes are from this file
Later it says:
Because the 4 individual (32 bit) RGB etc attributes, combine to make a 128 bit value.
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The 5 GHz controversy is because it IS (sort of) a 5GHz processor (AMD), but does not normally (no overclocking) go to 5 GHz on ALL cores, because the 5GHz is the turbo mode value, rather than the all cores running value.
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Quick and nasty explanation: tl;dr
Immediately after the spec sheet says "128 bit precision", it immediately says that it splits into 4 individual 32 bit values.
128-bit IEEE floating-point precision graphics pipeline
32-bit floating point color precision per component
Which I take to mean that the 128-bits are split into 4 lots of 32 bits.